The paper examines the relationship between the radio and X-ray luminosities of black holes, focusing on both stellar mass and supermassive black holes. The authors compile a sample of approximately 100 active galactic nuclei (AGN) with measured masses, 5 GHz core emission, and 2-10 keV luminosities, as well as 8 galactic black holes with simultaneous radio and X-ray observations. They find a significant correlation between radio luminosity (L_R) and both black hole mass (M) and X-ray luminosity (L_X). This relationship defines a "fundamental plane" in the three-dimensional space of log L_R, log L_X, and log M, given by the equation log L_R = (0.60^+0.11) log L_X + (0.78^+0.11) log M + 7.33^+4.05, with a scatter of σ_R = 0.88. The authors compare these results to theoretical relations derived by Heinz & Sunyaev (2003), which depend only on the assumed accretion model and the observed radio spectral index. They conclude that X-ray emission from black holes accreting at less than a few percent of the Eddington rate is unlikely to be produced by radiatively efficient accretion and is marginally consistent with optically thin synchrotron emission from the jet. On the other hand, models for radiatively inefficient accretion flows seem to agree well with the data. The paper discusses the implications of these findings for understanding black hole activity and the physics of accretion and jet production.The paper examines the relationship between the radio and X-ray luminosities of black holes, focusing on both stellar mass and supermassive black holes. The authors compile a sample of approximately 100 active galactic nuclei (AGN) with measured masses, 5 GHz core emission, and 2-10 keV luminosities, as well as 8 galactic black holes with simultaneous radio and X-ray observations. They find a significant correlation between radio luminosity (L_R) and both black hole mass (M) and X-ray luminosity (L_X). This relationship defines a "fundamental plane" in the three-dimensional space of log L_R, log L_X, and log M, given by the equation log L_R = (0.60^+0.11) log L_X + (0.78^+0.11) log M + 7.33^+4.05, with a scatter of σ_R = 0.88. The authors compare these results to theoretical relations derived by Heinz & Sunyaev (2003), which depend only on the assumed accretion model and the observed radio spectral index. They conclude that X-ray emission from black holes accreting at less than a few percent of the Eddington rate is unlikely to be produced by radiatively efficient accretion and is marginally consistent with optically thin synchrotron emission from the jet. On the other hand, models for radiatively inefficient accretion flows seem to agree well with the data. The paper discusses the implications of these findings for understanding black hole activity and the physics of accretion and jet production.